Electronic Version 19 (1994), 87-96

Judith L. Covington

A protopological group is a group G with a topology t with the property that there exists a collection N of normal subgroups such that (1) for every neighborhood U of the identity there exists N \in N such that N 'subset' U and (2) G/N with the quotient topology is a topological group for every N \in N. We say that N converges to the identity and call N a normal system. A t-protopological group is a protopological group with normal system N such that for all N \in N we have that UN is open. In this paper we examine basic properties of t-protopological groups. We introduce a method of describing the associated Graev topology for a protopological group. Finally, we prove that a compact Hausdorff t-protopological group is a topological group.

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volume 19: table of contents
topology proceedings Electronic Version